Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
const int N=1e6+7;
int n,p[N],f[N],c[N],ans[N];
inline int read(){
	int num=0; char g=getchar(); while(g<48||57<g) g=getchar();
	while(47<g&&g<58) num=(num<<1)+(num<<3)+g-48,g=getchar(); return num;
}
inline bool check(int a,int b,int c){
	return(a<b&&b<c)||(b<c&&c<a)||(c<a&&a<b);
}
int main(){
	n=read();
	for(int i=1;i<=n;i++) p[i]=read(),f[p[i]]=i;
	for(int i=n-1;i>0;i--){
		if(!ans[i+1]){
			if(f[i]>f[i+1]) ans[i]=1,c[i]=i+1;
		}
		else{
			if(check(f[i],f[i+1],f[c[i+1]])) ans[i]=ans[i+1],c[i]=c[i+1];
			else ans[i]=ans[i+1]+1,c[i]=i+1;
		}
	}
	cout<<ans[1]<<endl;
	return 0;
}